This analysis demonstrates that reduced twisted group C*-algebras of selfless groups are selfless, indicating strict comparison and purity.
We prove that any reduced twisted group C*-algebra of a selfless group with the rapid decay property is selfless. As an application, we show that twisted group C*-algebras of acylindrically hyperbolic groups (possibly with nontrivial finite radical) and rapid decay are pure, and hence have strict comparison.
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Raum et al. (2025) studied this question.
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